Edwards equations

Both the Edwards equation and Pearson s HSAB concept take as primary determinants of nucleophilicity the polarizability and basicity. A two-term equation of Bartoli and Todesco" uses these ideas also, but as a measure of polarizability the... 

The position of aniline in the above reactivity order deserves special comment. Aniline is less basic than pyridine by a relatively small factor, 0.65 pA units, but is appreciably more polarizable it then seems likely that the inverted order of reactivity is caused by the polarizability term in accordance with Edwards equation. If this is correct, in the reactivity order piperidine > aniline > pyridine, inversion with respect to basicity appears to result from an abnormally high reactivity of aniline rather than from a particularly low reactivity of pyridine. This view differs from that based on relative steric requirements of the reagents, but other factors besides basicity and polarizability may well contribute to the quantitative experimental picture. 

In Eq. (10-17), parameters a and b measure the sensitivity of the reaction to these nucleophilic parameters. Since H measures proton basicity and En the electron-donation ability, this treatment models nucleophilicity as a combination of electron loss and electron pair donation. The Edwards equation is thus an oxibase scale of nucleophilic reactivity. Table 10-5 summarizes the nucleophilic parameters. 

Edwards equation, 230-232 Electrical circuits, analogs to mechanisms, 138-139 Electron exchange, 243 Electrostatic effects, 203 Elementary reaction, 2, 4, 12, 55 rate of, 5... 

At the high polymer concentration used in plasticized systems the viscosity of amorphous polymer is given by the modified Rouse theory at low molecular weight, M - 2Mr [from equation (47)] and by the modified Doi-Edwards equation at high molecular weight. In the first case... 

This point was recognized quite early by Edwards (7) in correlating the rates at which H202 reacts with a series of nucleophiles. The Edwards equation... 

Second-order rate constants for the reactions of phenacyl bromide with a number of anionic or neutral nucleophiles in 3 2 (v/v) acetone-water have been measured at several temperatures.141 Correlation analysis with the Bronsted equation or Swain-Scott equation is not satisfactory. Better results were obtained with the two-parameter Edwards equation. 

The concept of soft and hard acids and bases (7), which is in effect an extension of the Chatt-Ahrland classification (2) of A and B metals, is applied in the 1963 paper by Pearson (7) particularly to equilibria involving mainly inorganic systems. This paper follows an earlier discussion by Edwards and Pearson (3) of the Swain-Edwards equation (4) (1) for nucleophilic reactivity. 

The degree of the orientational ordering in the swollen coil can be estimated using the Edwards equation (see Ref.24))... 

In terms of network analogy, the damping function may be viewed as the expression of the retraction of the strands as compared to the continuum. The Lodge model thus corresponds to no retraction (affine deformation, a=0 in equation (30) ), the Doi-Edwards equation corresponds to complete retraction (a=0.2), whereas incomplete retraction makes the damping function more softly decreasing (0 < a < 0.2). In the later cases, the deformation is non-affine since there is a difference between that of the continuum and that of the network strands. Wagner [33] showed that the Doi Edwards strain function... 

The Doi—Edwards equation is a special case of a separable K—BKZ equation, for which... 

This latter approximation shows that the strain dependence of the Doi-Edwards equation is softer than that of the temporary network model roughly by the factor 1 -p (7i — 3)/5, There is also a differential approximation to the Doi-Edwards equation (Marmcci 1984 Larson 1984b) ... 

The Doi— Edwards equation predicts that the ratio 2 is —2/7 = —0.29 at low shear rates. This changes to 4 2/ l i = —1/7 = —0.14 when the independent alignment approximation is dropped (Osaki et al. 1981). With or without the independent alignment approximation, the ratio —is predicted to decrease towards zero as the shear rate increases. The prediction of fof entangled solutions contrasts with that predicted... 

The Doi-Edwards equation predicts an overshoot in shear stress as a function of time after inception of steady shearing, but no overshoot in the first normal stress difference (Doi and Edwards 1978a). Typical overshoots in these quantities for a polydisperse melt are shown in Fig. 1-10. For monodisperse melts, the Doi-Edwards model predicts that the shear-stress maximum should occur at a shear strain yt = Yp, of about 2, roughly independently of... 

Problems 3.7 through 3.11 test your ability to work with reptation ideas and the Doi-Edwards equation. 

Problem 3.8 Numerically solve Eq. (3-78), the differential approximation to the Doi-Edwards equation for entangled linear melts, in a steady-state shearing flow. Plot the dimensionless shear stress ayijG against Weissenberg number W/ = )>r for Wi between 0.1 and 100. 

Problem 3,9 Integrate the Doi-Edwards equation (3-71) using the Currie expression for the Q tensor, Eq. (3-75), for steady-state shearing, for yr = 0.1, 0.3, 1.0, 3.0, and 10.0, using only one relaxation time in the spectrum. Plot the values of dimensionless shear stress OnjG versus yr on the same plot as in Problem 3.8. How close is the prediction of the approximate differential model to that of the exact integral model ... 

The Edwards equation sums component processes modelling the transfer of the pair of bonding electrons from substrate to product. The component model processes are proton transfer to the nucleophile (the proton affinity) (Equation 27) and the polarisability of the nucleophile as judged by its standard electrode potential (E ) (Equation 28). 

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